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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Ultrafast high-harmonic spectroscopy of solids

High-harmonic spectroscopy, an ultrafast all-optical technique initially conceptualized in atomic and molecular systems, has now emerged as a powerful platform for studying the structure and dynamics of condensed matter. Unlike that in the gas phase, solid-state high-harmonic generation relies on the fundamental response from high atomic density and periodicity, leading to interband transitions and coherent driving of electrons and holes in their respective bands. These mechanisms make high-harmonic spectroscopy particularly sensitive to the electronic band structure, topological properties and many-body correlations in condensed media. An advantage of high-harmonic spectroscopy over other spectroscopic methods is its ability to probe ultrafast phenomena, capturing femto- to attosecond dynamics of multi-band and strongly correlated electron interactions in solids. Furthermore, in this Review, we discuss the latest experimental and theoretical advances in ultrafast high-harmonic spectroscopy of solids and provide perspectives for future research in this field.

High-harmonic generation↗
DOE OSTI2023

Quantum-Path-Resolved Attosecond High-Harmonic Spectroscopy

Strong-field ionization of molecules releases electrons which can be accelerated and driven back to recombine with their parent ion, emitting high-order harmonics. This ionization also initiates attosecond electronic and vibrational dynamics in the ion, evolving during the electron travel in the continuum. Revealing this subcycle dynamics from the emitted radiation usually requires advanced theoretical modeling. Here we show that this can be avoided by resolving the emission from two families of electronic quantum paths in the generation process. The corresponding electrons have the same kinetic energy, and thus the same structural sensitivity, but differ by the travel time between ionization and recombination-the pump-probe delay in this attosecond self-probing scheme. We measure the harmonic amplitude and phase in aligned CO 2 and N 2 molecules and observe a strong influence of laser-induced dynamics on two characteristic spectroscopic features: a shape resonance and multichannel interference. This quantum-path-resolved spectroscopy thus opens wide prospects for the investigation of ultrafast ionic dynamics, such as charge migration.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2026

Isostructural electronic transition in MoS 2 probed by solid-state high-harmonic generation spectroscopy

Studying materials under extreme pressure in diamond anvil cells (DACs) is key to discovering emergent states of matter, yet no method currently allows the direct measurement of the electronic structure in this environment. Solid-state high-harmonic generation (sHHG) offers a unique all-optical window into the electronic structure of materials. We demonstrate sHHG spectroscopy inside a DAC by probing 2H-MoS 2 , up to 30 GPa, revealing a pressure-induced crossover of the lowest direct bandgap from the K-point to the Γ-point. This transition manifests as a sharp minimum in harmonic intensity and a 30° rotation of the sHHG polarization anisotropy, despite the absence of a structural phase change. First-principles simulations attribute these features to interference between competing excitation pathways at distinct points in the Brillouin zone. Our results establish sHHG as a sensitive probe of electronic transitions at high pressure, enabling access to quantum phenomena that evade detection by conventional techniques.

Nebgen, Bailey R. [University of California, Berke↗
DOE OSTI2023

Attosecond probing and control of charge migration in carbon-chain molecule

In quantum mechanics, when an electron is quickly ripped off from a molecule, a superposition of new eigenstates of the cation creates an electron wave packet that governs the charge flow inside, which has been called charge migration (CM). Experimentally, extracting such dynamics at its natural (attosecond) timescale is quite difficult. We report the first such experiment in a linear carbon-chain molecule, butadiyne (C 4 H 2 ), via high-harmonic spectroscopy (HHS). By employing advanced theoretical and computational tools, we showed that the wave packet and the CM of a single molecule are reconstructed from the harmonic spectra for each fixed-in-space angle of the molecule. For this one-dimensional molecule, we calculate the center of charge $\langle$ x $\rangle$ ( t ) to obtain v cm , to quantify the migration speed and how it depends on the orientation angle. The findings also uncover how the electron dynamics at the first few tens to hundreds of attoseconds depends on molecular structure. The method can be extended to other molecules where the HHS technique can be employed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

A tutorial on high-order harmonic generation in atoms, molecules, and condensed matter

This tutorial introduces strong-field-driven high-order harmonics, their experimental generation and characterization techniques, and their main applications including attosecond pulse generation and ultrafast spectroscopy of the target material. We begin from the use of atomic targets, where the first high-order harmonic generation (HHG) experiments were realized in the late 1980s. Then, we briefly discuss the basics of the microscopic generation mechanism and how various steps of the mechanism were exploited in applications such as generating isolated attosecond pulses and probing molecular orbitals. We introduce and describe the standard experimental approaches for condensed phase HHG, where we discuss unique technical challenges of the use of solid-state materials, such as the mitigation of plasma formation and laser damage. We cover the fundamentals of high-harmonic spectroscopy in condensed matter systems, such as wide bandgap dielectrics, semiconductors, liquid media, and 2D-crystals. We provide some examples of rapidly emerging spectroscopic capabilities, such as for probing crystal symmetries, Berry phases, and associated non-trivial topological properties of the source material. Finally, we provide an overview of the research field, including some of the challenges, opportunities, and open questions.

Attosecond pulses↗
DOE OSTI2023

A versatile high-average-power ultrafast infrared driver tailored for high-harmonic generation and vibrational spectroscopy

We report on an ultrafast infrared optical parametric chirped-pulse amplifier (OPCPA), pumped by a 200-W thin-disk Yb-based regenerative amplifier at a repetition rate of 100 kHz. The OPCPA is tunable in the spectral range 1.4–3.9 μm, generating up to 23 W of < 100-fs signal and 13 W of < 200-fs idler pulses for infrared spectroscopy, with additional spectral filtering capabilities for Raman spectroscopy. The OPCPA can also yield 19 W of 49-fs 1.75- μm signal or 5 W of 62-fs 2.8- μm idler pulses with active carrier-to-envelope-phase (CEP) stabilisation for high-harmonic generation (HHG). We illustrate the versatility of the laser design, catering to various experimental requirements for probing ultrafast science.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Electro-optic sampling of classical and quantum light

Full characterization of electric-field waveforms in amplitude and phase is achieved across the terahertz to visible spectral range through interaction with an optical pulse shorter than a half-cycle period via the Pockels (linear electro-optic) effect. This technique of electro-optic sampling has become an indispensable tool in various areas, including ultrafast pump-probe, time-domain and frequency-comb spectroscopies, quantum optics, high-harmonic generation, and attosecond science, and holds great promise for further advances. Not only does it enable spectroscopic measurements with record dynamic range and temporal resolution, along with massively parallel real-time spectral data acquisition, but its remarkable sensitivity also allows the detection of vacuum fluctuations, i.e., “zero-point motion” of electric fields, profoundly impacting our understanding of the fundamental laws of nature.

Benea-Chelmus, Ileana-Cristina (ORCID:000000024814↗
DOE OSTI2024

High-harmonic spin-shearing interferometry for spatially resolved EUV magneto-optical spectroscopy

We present a method for achieving hyperspectral magnetic imaging in the extreme ultraviolet (EUV) region based on high-harmonic generation (HHG). By interfering two mutually coherent orthogonally-polarized and laterally-sheared HHG sources, we create an EUV illumination beam with spatially-dependent ellipticity. By placing a magnetic sample in the beamline and sweeping the relative time delay between the two sources, we record a spatially resolved interferogram that is sensitive to the EUV magnetic circular dichroism of the sample. This image contains the spatially-resolved magneto-optical response of the sample at each harmonic order, and can be used to measure the magnetic properties of spatially inhomogeneous magnetic samples.

Optics↗
DOE OSTI2025

Open-source simulation program for extreme ultraviolet and soft x-ray sources based on high-harmonic generation

Light sources based on high-harmonic generation (HHG) underpin ultrafast spectroscopy experiments across a large range of photon energies, spanning from the extreme ultraviolet to the soft x-ray. To this day, their design, implementation, and improvement presens unique challenges, but can be aided by numerical tools. Here we present a new simulation program designed for this purpose, which takes both macroscopic and microscopic aspects of high-harmonic generation into account and is therefore applicable across the broad range of parameters which HHG based light sources are today utilized. The program is validated by comparison with published experimental results and by calculating harmonic emission in four common experimental configurations.

Femtosecond lasers↗
DOE OSTI2022

Single crystal growth of iridates without platinum impurities

Iridates have attracted much interest in the last decade for their novel magnetism emerging in the limit of strong spin-orbit coupling and possible unconventional superconductivity. A standard for growing iridate single crystals has been the flux method using platinum crucibles. Here, in this work, we show that this widely used method compromises the sample quality by inclusion of platinum impurities. We find that Sr 2 ⁢IrO 4 single crystals grown in iridium crucibles show remarkable differences from those grown in platinum crucibles in their sample characterizations using Raman spectroscopy, resistivity, magnetization, optical third harmonic generation, resonant x-ray diffraction, and resonant inelastic x-ray scattering measurements. In particular, we show that several peaks of sizable intensities disappear in the Raman spectra of samples free of platinum impurities, and a significantly larger activation energy is extracted from the resistivity data compared to previously reported values. Furthermore, we find no evidence of the previously reported glide-symmetry-breaking structural distortions and confirm the I⁢ 4 1 / acd space group of the lattice symmetry. Although the platinum impurities are not apparent in the magnetic properties and thus went unnoticed in the stoichiometric insulating phase for a long time, their effects can be much more detrimental to transport properties in chemically doped compounds. Therefore, our result suggests using growth methods that avoid platinum impurities for an investigation of the intrinsic physical properties of iridates, and possible superconducting phases.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Attosecond Transient Grating Spectroscopy with Near-Infrared Grating Pulses and an Extreme Ultraviolet Diffracted Probe

Transient grating spectroscopy has become a mainstay among metal and semiconductor characterization techniques. Here, we extend the technique toward the shortest achievable time scales by using tabletop high-harmonic generation of attosecond extreme ultraviolet (XUV) pulses that diffract from transient gratings generated with sub-5 fs near-infrared (NIR) pulses. We demonstrate the power of attosecond transient grating spectroscopy (ATGS) by investigating the ultrafast photoexcited dynamics in an Sb semimetal thin film. ATGS provides an element-specific, background-free signal unfettered by spectral congestion, in contrast to transient absorption spectroscopy. With ATGS measurements in Sb polycrystalline thin films, we observe the generation of coherent phonons and investigate the lattice and carrier dynamics. Among the latter processes, we extract carrier thermalization, hot carrier cooling, and electron-hole recombination, which are on the order of 20 fs, 50 fs, and 2 ps time scales, respectively. Furthermore, the simultaneous collection of transient absorption and transient grating data allows us to extract the total complex dielectric constant in the sample dynamics with a single measurement, including the real-valued refractive index, from which we are also able to investigate carrier-phonon interactions and longer-lived phonon dynamics. The outlined experimental technique expands the capabilities of transient grating spectroscopy and attosecond spectroscopies by providing a wealth of information concerning carrier and lattice dynamics with an element-selective technique at the shortest achievable time scales.

Quintero-Bermudez, Rafael↗
DOE OSTI2023

Signatures of the Bromine Atom and Open-Shell Spin Coupling in the X-ray Spectrum of the Bromobenzene Cation

Tabletop X-ray spectroscopy measurements at the carbon K-edge complemented by ab initio calculations are used to investigate the influence of the bromine atom on the carbon core–valence transitions in the bromobenzene cation (BrBz + ). The electronic ground state of the cation is prepared by resonance-enhanced two-photon ionization of neutral bromobenzene (BrBz) and probed by X-rays produced by high-harmonic generation (HHG). Replacing one of the hydrogen atoms in benzene with a bromine atom shifts the transition from the 1s C* orbital of the carbon atom (C*) bonded to bromine by ~1 eV to higher energy in the X-ray spectrum compared to the other carbon atoms (C). Moreover, in BrBz + , the X-ray spectrum is dominated by two relatively intense transitions, 1s C →π* and 1s C* →σ*(C*–Br), where the second transition is enhanced relative to the neutral BrBz. In addition, a doublet peak shape for these two transitions is observed in the experiment. The 1s C →π* doublet peak shape arises due to the spin coupling of the unpaired electron in the partially vacant π orbital (from ionization) with the two other unpaired electrons resulting from the transition from the 1s C core orbital to the fully vacant π* orbitals. Here, the 1s C* →σ* doublet peak shape results from several transitions involving σ* and vibrational C*–Br mode activations following the UV ionization, which demonstrates the impact of the C*–Br bond length on the core–valence transition as well as on the relaxation geometry of BrBz + .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

State-selective probing of CO 2 autoionizing inner valence Rydberg states with attosecond extreme ultraviolet four-wave-mixing spectroscopy

Nonlinear spectroscopies can disentangle spectra that are congested due to inhomogeneous broadening. Here, in conjunction with theoretical calculations, attosecond extreme ultraviolet (XUV) four-wave-mixing (FWM) spectroscopy is utilized to probe the dynamics of autoionizing inner valence excited Rydberg states of the polyatomic molecule, CO 2 . This tabletop nonlinear technique employs a short attosecond XUV pulse train and two noncollinear, few-cycle near-infrared pulses to generate background-free XUV wave-mixing signals. FWM emission is observed from the n=5-7 states of the Henning sharp ndσ g Rydberg series that converges to the ionic $\widetilde{B}$ 2 Σ$^{+}_{u}$ state. However, these transient emission signals decay with lifetimes of 33 ± 6, 53 ± 2, and 94 ± 2 fs, respectively, which calculations show are consistent with the lifetimes of the short-lived n=6-8 members of the nsσ g character Henning diffuse Rydberg series. The oscillator strengths of transitions between states involved in all possible resonant FWM processes are calculated, verifying that the nonlinear spectra are dominated by pathways described by an initial excitation to the diffuse nsσ g Rydberg series and emission from the sharp ndσ g Rydberg series. The results substantiate not only that attosecond XUV FWM spectroscopy produces rigorous and meaningful measurements of ultrafast dynamics in polyatomic systems, but also that nonlinear spectroscopic techniques are versatile tools to selectively probe dynamics that are otherwise difficult to access.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

M-Edge Spectroscopy of Transition Metals: Principles, Advances, and Applications

M-edge X-ray absorption spectroscopy (XAS), which probes 3p→3d transitions in first-row transition metals, provides detailed insights into oxidation states, spin-states, and local electronic structure with high element and orbital specificity. Operating in the extreme ultraviolet (XUV) region, this technique provides sharp multiplet-resolved features with high sensitivity to ligand field and covalency effects. Compared to K- and L-edge XAS, M-edge spectra exhibit significantly narrower full widths at half maximum (typically 0.3–0.5 eV versus >1 eV at the L-edge and >1.5–2 eV at the K-edge), owing to longer 3p core-hole lifetimes. M-edge measurements are also more surface-sensitive due to the lower photon energy range, making them particularly well-suited for probing thin films, interfaces, and surface-bound species. The advent of tabletop high-harmonic generation (HHG) sources has enabled femtosecond time-resolved M-edge measurements, allowing direct observation of ultrafast photoinduced processes such as charge transfer and spin crossover dynamics. This review presents an overview of the fundamental principles, experimental advances, and current theoretical approaches for interpreting M-edge spectra. We further discuss a range of applications in catalysis, materials science, and coordination chemistry, highlighting the technique’s growing impact and potential for future studies.

M-edge XANES↗
DOE OSTI2023

Nonresonant coherent amplitude transfer in attosecond four-wave-mixing spectroscopy

Attosecond four-wave mixing (FWM) spectroscopy using an extreme ultraviolet (XUV) pulse and two noncollinear near-infrared (NIR) pulses is employed to measure Rydberg wave packet dynamics resulting from XUV excitation of a 3s electron in atomic argon into a series of autoionizing 3s –1 np Rydberg states ~29 eV. The emitted signals from individual Rydberg states exhibit oscillatory structure and persist well beyond the expected lifetimes of the emitting Rydberg states. These results reflect substantial contributions of longer-lived Rydberg states to the FWM emission signals of each individually detected state. A wave packet decomposition analysis reveals that coherent amplitude transfer occurs predominantly from photoexcited 3s –1 (n + 1) p states to the observed 3s –1 np Rydberg states. The experimental observations are reproduced by time-dependent Schrödinger equation simulations using electronic structure and transition moment calculations. Finally, the theory highlights that coherent amplitude transfer is driven nonresonantly to the 3s –1 np states by the NIR light through 3s –1 (n + 1)s and 3s –1 (n – 1)d dark states during the FWM process.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Giant room-temperature nonlinearities in a monolayer Janus topological semiconductor

Abstract Nonlinear optical materials possess wide applications, ranging from terahertz and mid-infrared detection to energy harvesting. Recently, the correlations between nonlinear optical responses and certain topological properties, such as the Berry curvature and the quantum metric tensor, have attracted considerable interest. Here, we report giant room-temperature nonlinearities in non-centrosymmetric two-dimensional topological materials—the Janus transition metal dichalcogenides in the 1 T’ phase, synthesized by an advanced atomic-layer substitution method. High harmonic generation, terahertz emission spectroscopy, and second harmonic generation measurements consistently show orders-of-the-magnitude enhancement in terahertz-frequency nonlinearities in 1 T’ MoSSe (e.g., > 50 times higher than 2 H MoS 2 for 18 th order harmonic generation; > 20 times higher than 2 H MoS 2 for terahertz emission). We link this giant nonlinear optical response to topological band mixing and strong inversion symmetry breaking due to the Janus structure. Our work defines general protocols for designing materials with large nonlinearities and heralds the applications of topological materials in optoelectronics down to the monolayer limit.

42 ENGINEERING↗
DOE OSTI2023

Ultrafast nonequilibrium dynamics and high-harmonic generation in two-dimensional quantum spin Hall materials

For this work, we develop the theoretical framework of nonequilibrium ultrafast photonics in monolayer quantum spin Hall insulators supporting a multitude of topological states. In these materials, ubiquitous strong light-matter interactions in the femtosecond scale lead to nonadiabatic quantum dynamics, resulting in topology-dependent nonlinear optoelectronic transport phenomena. We investigate the mechanism driving topological Dirac fermions interacting with strong ultrashort light pulses and uncover various experimentally accessible physical quantities that encode fingerprints of the quantum material's topological electronic state from the high-harmonic generated spectrum. Our work sets the theoretical cornerstones to realize the full potential of time-resolved harmonic spectroscopy for understanding nonequilibrium processes in quantum topological systems and identifying topological invariants in two-dimensional quantum spin Hall solid state systems.

2-dimensional systems↗